Just a note that there's a relatively fail-safe way to avoid concerns about rushing pqcrypto too soon: Just couple it with established crypto.
This is e.g. what google is doing in all their pqcrypto experiments. They use an elliptic curve key exchange combined with a post quantum key exchange. If you don't do any really big mistakes you get at lest the security of the stronger of the two.
Given that elliptic curve crypto is really cheap such a combination will probably be used for most post quantum schemes for a while.
Eventually quantum computing will also be really cheap. I don't think it'll take all that much time, given the amount of money and attention.
Thinking of security in layers, as you've suggested, is the way to go. Secure communications has always been about being "too expensive" to decrypt in a relevant time span.
Just because there's a new kid on the block, we need to keep our old friends around.
This is e.g. what google is doing in all their pqcrypto experiments. They use an elliptic curve key exchange combined with a post quantum key exchange. If you don't do any really big mistakes you get at lest the security of the stronger of the two.
Given that elliptic curve crypto is really cheap such a combination will probably be used for most post quantum schemes for a while.